Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <cstdio>
int N, p[200001], O, f, E;
inline bool Order(int p1, int p2, int pf)
{
	return pf < p1 && p1 < p2 || p1 < p2 && p2 < pf || p2 < pf && pf < p1;
}
int main()
{
	scanf("%d", &N);
	for (int i = 1, x; i <= N; i++)
	{
		scanf("%d", &x);
		p[x] = i;
	}
	E = N;
	while (E > 1 && p[E - 1] < p[E])
		E--;
	if (E == 1)
	{
		puts("0");
		return 0;
	}
	int f = E--, O = 1;
	for (int i = E - 1; i; i--)
		if (!Order(p[i], p[i + 1], p[f]))
		{
			f = i + 1;
			O++;
		}
	printf("%d\n", O);
	return 0;
}